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  \begin{center}
    \textbf{ONLINE APPENDIX} \\
    \vspace{4mm}
    For the paper: \\
     \vspace{6mm}
            {\large \textsc{The Twin Instrument: \\ Fertility and Human Capital Investment}} \\
            \vspace{3mm}
            Sonia Bhalotra and Damian Clarke
  \end{center}


\setlength{\parskip}{1em}
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\newpage
\section{Appendix Figures and Tables}
\begin{figure}[htpb!]
  \begin{center}
    \caption{Education and Fertility Trends (USA)}
    \label{TWINfig:USATrends}
    \includegraphics[scale=0.92]{./results/added/USTrends.eps}
    \vspace{-8mm}
    \floatfoot{Notes to Figure \ref{TWINfig:USATrends}: Trends in fertility and education
      are compiled from the World Bank databank and the American Community Surveys (ACS),
      respectively.  Trends in fertility are directly reported by the World Bank as completed
      fertility per woman were she exposed to prevailing rates in a given year for her whole
      fertile life.  Education is calculated using all women aged over 25 years in the ongoing
      ACS (2001-2013) collected by the United States Census Bureau.  The figure presents
      average completed education for all women aged 25 in the year in question.}
  \end{center}
\end{figure}

\begin{figure}[htpb!]
  \centering
  \begin{subfigure}{.5\textwidth}
    \centering
    \includegraphics[scale=0.53]{./results/figures/ferttrend_35_all.eps}
    \caption{Trends in Fertility}

    \label{TWINfig:fertrend}
  \end{subfigure}%
  \begin{subfigure}{.5\textwidth}
    \centering
    \includegraphics[scale=0.52]{./results/figures/eductrend_all.eps}
    \caption{Trend in Education}
    \label{TWINfig:eductrend}
  \end{subfigure}
  \caption{Education and Fertility (Developing Countries)}
  \label{TWINfig:trends}
  \floatfoot{Notes to Figure \ref{TWINfig:trends}: Cohorts are made up of all individuals
    from the DHS who are aged over 35 years (for fertility), and over 15 years (for education).
    In each case the sample is restricted to those who have approximately completed fertility
    and education respectively.  Full summary statistics for these variables are provided
    in Table \ref{TWINtab:sumstats}, and a full list of country and survey years are
    available in Table \ref{TWINtab:countries}.}
\end{figure}

\begin{figure}[htpb!]
  \begin{center}
    \caption{Birth Size of Twins versus Singletons (Developing Countries)}
    \label{TWINfig:Size}
    \includegraphics[scale=0.82]{./results/figures/Size.eps}
  \end{center}
  \vspace{-4mm}
  \floatfoot{Notes to Figure \ref{TWINfig:Size}: Estimation sample consists of all
    surveyed births from DHS countries occurring within 5 years prior to the date of
    the survey.  For each of these births, all mothers retrospectively report the
    (subjective) size of the baby at the time of birth.}
\end{figure}

\begin{figure}[htpb!]
  \begin{center}
    \caption{Birth Weight of Twins versus Singletons (USA)}
    \label{TWINfig:SizeUS}
    \includegraphics[scale=0.82]{./results/added/birthweightUSA.eps}
  \end{center}
  \vspace{-4mm}
  \floatfoot{Notes to Figure \ref{TWINfig:SizeUS}: Estimation sample consists of all
    non-ART births from NVSS data between 2009 and 2013.  Birthweights below 500 grams
    and above 6,500 grams are trimmed from the sample.}
\end{figure}

\begin{figure}[htpb!]
  \centering
  \begin{subfigure}{.5\textwidth}
    \centering
    \includegraphics[scale=0.6]{./results/added/twinBordUSA.eps}
    \caption{United States}
    \label{TWINfig:bordUS}
  \end{subfigure}%
  \begin{subfigure}{.5\textwidth}
    \centering
    \includegraphics[scale=0.6]{./results/figures/twinbybord.eps}
    \caption{Developing Countries}
    \label{TWINfig:bordDHS}
  \end{subfigure}
  \caption{Proportion of Twins by Birth Order}
  \label{TWINfig:bord}
  \floatfoot{Notes to Figure \ref{TWINfig:bord}: The fraction of twin births is calculated
    from the full sample of non-ART users in NVSS data from 2009-2013 (panel A), and the
    full sample of DHS data (panel B).  The solid line represents
    the average fraction of twins in the full sample (2.89\% in US, 1.85\% in DHS), while
    the dotted line presents twin frequency by birth order.  The dotted line joins points
    at each birth order.  Birth orders greater than 6 (USA) and 10 (DHS) are removed, as
    they account for less than 1\% of all recorded births.}
\end{figure}

\begin{figure}[htpb!]
  \begin{center}
    \caption{Reading with Children at Ages 6-9 and Future School Completion Rates}
    \label{investmentCompletion}
    \includegraphics[scale=0.8]{./results/figures/behindCohortReading.eps}
    \vspace{-8mm}
    \floatfoot{Notes to Figure \ref{investmentCompletion}: Each point estimate and 95\% confidence interval displays the coefficient from a separate regression of whether an individual is behind their cohort at age $x\in\{10,\ldots,18\}$ on whether the parent frequently read with the child between the ages of 6--9 years. All remaining details are identical to those in Figure \ref{NLSYcompletionHGC}.}
  \end{center}
\end{figure}

\begin{landscape}
\begin{figure}[htpb!]
  \centering
  \begin{subfigure}{.33\textwidth}
    \centering
    \includegraphics[scale=1.1]{./results/figures/fert_twoplus.eps}
    \caption{Two-Plus Group}
    \label{TWINfig:fert2}
  \end{subfigure}%
  \begin{subfigure}{.33\textwidth}
    \centering
    \includegraphics[scale=1.1]{./results/figures/fert_threeplus.eps}
    \caption{Three-Plus Group}
    \label{TWINfig:fert3}
  \end{subfigure}%
  \begin{subfigure}{.33\textwidth}
    \centering
    \includegraphics[scale=1.1]{./results/figures/fert_fourplus.eps}
    \caption{Four-Plus Group}
    \label{TWINfig:fert4}
  \end{subfigure}
  \caption{Total Family Size in Analysis Samples}
  \label{TWINfig:fertsize}
  \floatfoot{Notes to Figure \ref{TWINfig:fertsize}: Histograms display the total
    family size of families meeting inclusion criteria for each estimation
    sample (two-plus, three-plus, and four-plus). By definition, the two-plus sample
    only includes families with at least two births, the three-plus sample only
    includes families with at least three births, and the four-plus sample only
  includes families with at least four births.}
\end{figure}
\end{landscape}

\begin{figure}[htpb!]
  \begin{center}
    \caption{Density Test of Instrumental Validity from \citet{Kitagawa2015}}
    \label{TWINfig:Kitagawa}
    \includegraphics[scale=0.5]{./results/added/Kitagawa_DHS_two.eps}
    \vspace{-8mm}
    \floatfoot{Notes to Figure \ref{TWINfig:Kitagawa}: Kernel density plots document the sub-densities of the outcome variable of interest in IV regressions (school Z-score) for children preceding twins and for children not preceding twins in the 2+ sample.  ``Treated'' refers to families with at least 3 children, and so both densities document frequencies only for this group.  The \citet{Kitagawa2015} test consists of determining whether the two densities intersect, with intersection being evidence of instrumental \emph{in}validity. We follow Kitagawa in using a Gaussian kernel and bandwidth of 0.08.  Outliers are suppressed from the graph to ease visualisation of the sub-densities.  Results for the full version of the test including controls along with p-values associated with instrumental invalidity are presented in Table \ref{tab:Kitagawa}.}
  \end{center}
\end{figure}

\begin{figure}[htpb!]
  \centering
  \begin{subfigure}{.5\textwidth}
    \centering
    \includegraphics[scale=0.58]{./results/figures/boundsNHIS_EducationZscore.eps}
    \caption{Education Z-Score}
    \label{TWINfig:boundsUSed}
  \end{subfigure}%
  \begin{subfigure}{.5\textwidth}
    \centering
    \includegraphics[scale=0.58]{./results/figures/boundsNHIS_excellentHealth.eps}
    \caption{Excellent Health}
    \label{TWINfig:boundsUSHealth}
  \end{subfigure}
  \caption{Parameter and Bound Estimates of the Q--Q Trade-off (USA)}
  \label{TWINfig:boundsUS}
  \floatfoot{Notes to Figure \ref{TWINfig:boundsUS}: Refer to notes to Figure \ref{TWINfig:DHSbounds}. Identical bounds are presented, but in this case based on NHIS data (with considerably fewer observations).}
\end{figure}

\begin{figure}[htpb!]
  \begin{center}
    \caption{Plausibly Exogenous Bounds: (USA, 3+ Sample)}
    \label{TWINfig:PEx-USA}
    \begin{subfigure}{.5\textwidth}
      \centering
      \includegraphics[scale=0.6]{./results/figures/ConleyUSA_excellentHealth_three.eps}
      \caption{Excellent Health}
      \label{TWINfig:HPEx-USA2}
    \end{subfigure}%
    \begin{subfigure}{.5\textwidth}
      \centering
      \includegraphics[scale=0.6]{./results/figures/ConleyUSA_EducationZscore_three.eps}
      \caption{Education Z-Score}
      \label{TWINfig:PEx-USA2}
    \end{subfigure}
  \end{center}
  \floatfoot{Notes to Figure \ref{TWINfig:PEx-USA}: See notes to Figure
    \ref{TWINfig:ltz3}. An identical approach is employed, however now using USA
    (NHIS) data.}
\end{figure}


\begin{landscape}
\begin{figure}[htpb!]
  \begin{center}
    \caption{Plausibly Exogenous Bounds: School Z-Score (Developing Countries Alternative Parity Estimates)}
    \label{TWINfig:PEx-DHS2}
    \begin{subfigure}{.33\textwidth}
      \centering
      \includegraphics[scale=0.6]{./results/figures/LTZ_pooled.eps}
      \caption{Pooled Bounds}
      \label{TWINfig:ltzp}
    \end{subfigure}%
    \begin{subfigure}{.33\textwidth}
      \centering
      \includegraphics[scale=0.6]{./results/figures/LTZ_two.eps}
      \caption{Two Plus}
      \label{TWINfig:ltz2}
    \end{subfigure}
    \begin{subfigure}{.33\textwidth}
      \centering
      \includegraphics[scale=0.6]{./results/figures/LTZ_four.eps}
      \caption{Four Plus}
      \label{TWINfig:ltz4}
    \end{subfigure}
  \end{center}
  \floatfoot{Notes to Figure \ref{TWINfig:PEx-DHS2}: Refer to notes to Figure \ref{TWINfig:ltz3} of the main text.}
\end{figure}
\end{landscape}

\begin{landscape}
\begin{figure}[htpb!]
  \begin{center}
    \caption{Plausibly Exogenous Bounds: (USA Alternative Parity Estimates)}
    \label{TWINfig:HPEx-USA}
    \begin{subfigure}{.33\textwidth}
      \centering
      \includegraphics[scale=0.6]{./results/figures/LTZ_NHIS_excellentHealth_pooled.eps}
      \caption{Excellent Health (Pooled)}
      \label{TWINfig:HPEx-USA2}
    \end{subfigure}%
    \begin{subfigure}{.33\textwidth}
      \centering
      \includegraphics[scale=0.6]{./results/figures/ConleyUSA_excellentHealth_two.eps}
      \caption{Excellent Health (2+)}
      \label{TWINfig:HPEx-USA3}
    \end{subfigure}
    \begin{subfigure}{.33\textwidth}
      \centering
      \includegraphics[scale=0.6]{./results/figures/ConleyUSA_excellentHealth_four.eps}
      \caption{Excellent Health (4+)}
      \label{TWINfig:HPEx-USA4}
    \end{subfigure}

    \begin{subfigure}{.33\textwidth}
      \centering
      \includegraphics[scale=0.6]{./results/figures/LTZ_NHIS_EducationZscore_pooled.eps}
      \caption{Education Z-Score (Pooled)}
      \label{TWINfig:HPEd-USA2}
    \end{subfigure}%
    \begin{subfigure}{.33\textwidth}
      \centering
      \includegraphics[scale=0.6]{./results/figures/ConleyUSA_EducationZscore_two.eps}
      \caption{Education Z-Score (2+)}
      \label{TWINfig:PEd-USA3}
    \end{subfigure}
    \begin{subfigure}{.33\textwidth}
      \centering
      \includegraphics[scale=0.6]{./results/figures/ConleyUSA_EducationZscore_four.eps}
      \caption{Education Z-Score (4+)}
      \label{TWINfig:PEd-USA4}
    \end{subfigure}
  \end{center}
  \floatfoot{Notes to Figure \ref{TWINfig:HPEx-USA}: Refer to notes to Figure \ref{TWINfig:ltz3} of the main text.}
\end{figure}
\end{landscape}

\begin{figure}[htpb!]
  \begin{center}
    \caption{IV Bounds Adding the Sex Mix Instrument for Fertility (Developing Countries)}
    \label{fig:DHSboundswSexMix}
    \includegraphics[scale=0.9]{./results/figures/boundsDHS_wPooledSameSex.eps}
    \vspace{-8mm}
    \floatfoot{Notes: Refer to notes to Figure \ref{TWINfig:DHSbounds}.  Identical bounds are estimated, however here fertility is instrumented by both twin birth, and the ``same sex instrument'' indicating whether the first $N$ births are of an identical sex for each of the $N$+ samples.  In bounding procedures, the same priors for twin birth are used, and priors for the same sex instrument assume that it is a valid instrument.}
  \end{center}
\end{figure}
\hspace{2cm}

\begin{figure}[htpb!]
  \begin{center}
    \caption{IV Bounds Adding the Sex Mix Instrument for Fertility (USA)}
    \label{fig:NHISboundswSexMix}
    \begin{subfigure}{.5\textwidth}
      \centering
      \includegraphics[scale=0.5]{./results/figures/boundsNHIS_EducationZscore_wPooledSameSex.eps}
      \caption{Education Z-Score}
      \label{fig:NHISboundswSexMix_Ed}
    \end{subfigure}%
    \begin{subfigure}{.5\textwidth}
      \centering
      \includegraphics[scale=0.5]{./results/figures/boundsNHIS_excellentHealth_wPooledSameSex.eps}
      \caption{Excellent Health}
      \label{fig:NHISboundswSexMix_EH}
    \end{subfigure}
  \end{center}
  \floatfoot{Notes: Refer to notes to Figure \ref{TWINfig:boundsUS} and \ref{fig:DHSboundswSexMix}.}
\end{figure}

\clearpage
\input{./results/added/Countries.tex}

\input{./results/added/SummaryStatistics.tex}

\input{./results/added/literature.tex}

\begin{landscape}
  \input{./results/tables/OLS-bord.tex}
\end{landscape}

\begin{landscape}
\input{./results/tables/NHISOLSBordEducationZscore.tex}
\end{landscape}

\begin{table}
  \caption{Full Output on Health and Socioeconomic Controls from IV Estimates (Developing Countries)}
  \label{FullIVDHS}
  \begin{tabular}{lcccccc}\toprule
    Dependent Variable  & \multicolumn{2}{c}{2+}& \multicolumn{2}{c}{3+}& \multicolumn{2}{c}{4+} \\ \cmidrule(r){2-3}\cmidrule(r){4-5}\cmidrule(r){6-7}
    School Z-Score& +H &+S\&H& +H &+S\&H& +H &+S\&H\\ \midrule
    \input{./results/tables/DHSIV_full.tex} \midrule
    \multicolumn{7}{p{18.4cm}}{{\footnotesize Notes: Full output is presented from IV regressions displayed in Table \ref{TWINtab:DHSall} on health and socioeconomic controls from models denoted ``+H'' (adding health controls) and ``+S\&H'' (adding health and socioeconomic controls).  Additionally, fixed effects for years of education of the mother are included in regressions though are not displayed in the interests of space.  These fixed effects show a positive gradient with higher education associated with additional child education.  Full notes are available in Table \ref{TWINtab:DHSall}.}} \\ \bottomrule
  \end{tabular}
\end{table}

\begin{table}
  \caption{Full Output on Health and Socioeconomic Controls from IV Estimates (USA Education)}
  \label{FullIVNHISeduc}
  \begin{tabular}{lcccccc}\toprule
    Dependent Variable  & \multicolumn{2}{c}{2+}& \multicolumn{2}{c}{3+}& \multicolumn{2}{c}{4+} \\ \cmidrule(r){2-3}\cmidrule(r){4-5}\cmidrule(r){6-7}
    School Z-Score& +H &+S\&H& +H &+S\&H& +H &+S\&H\\ \midrule
    \input{./results/tables/NHISIV_fullEducationZscore.tex} \midrule
    \multicolumn{7}{p{17.4cm}}{{\footnotesize Notes: Full output is presented from IV regressions displayed in Table \ref{TWINtab:NHISAll} on health and socioeconomic controls from models denoted ``+H'' (adding health controls) and ``+S\&H'' (adding health and socioeconomic controls).  Additionally, fixed effects for years of education of the mother are included in regressions though are not displayed in the interests of space.  These fixed effects show a positive gradient with higher education associated with additional child education.  Full notes are available in Table \ref{TWINtab:NHISAll}.}} \\ \bottomrule
  \end{tabular}
\end{table}

\begin{table}
  \caption{Full Output on Health and Socioeconomic Controls from IV Estimates (USA Health)}
  \label{FullIVNHISHealth}
  \begin{tabular}{lcccccc}\toprule
    Dependent Variable  & \multicolumn{2}{c}{2+}& \multicolumn{2}{c}{3+}& \multicolumn{2}{c}{4+} \\ \cmidrule(r){2-3}\cmidrule(r){4-5}\cmidrule(r){6-7}
    Excellent Health& +H &+S\&H& +H &+S\&H& +H &+S\&H\\ \midrule
    \input{./results/tables/NHISIV_fullexcellentHealth.tex} \midrule
    \multicolumn{7}{p{17.6cm}}{{\footnotesize Notes: Full output is presented from IV regressions displayed in Table \ref{TWINtab:NHISAll} on health and socioeconomic controls from models denoted ``+H'' (adding health controls) and ``+S\&H'' (adding health and socioeconomic controls).  Additionally, fixed effects for years of education of the mother are included in regressions though are not displayed in the interests of space.  These fixed effects show a positive gradient with higher education associated with additional child education.  Full notes are available in Table \ref{TWINtab:NHISAll}.}} \\ \bottomrule
  \end{tabular}
\end{table}

\begin{table}
  \caption{First Stages for Non-Linear IV Estimates}
  \label{TWINtab:nonlinearFirst}
  \begin{center}
    \begin{tabular}{lcccc}
      \toprule
      Instrument & Siblings $\geq$ 2 & Siblings $\geq$ 3 & Siblings $\geq$ 4 & Siblings $\geq$ 5 \\ \midrule
      \multicolumn{5}{l}{\textbf{Panel A: Two Plus Sample}} \\
      \input{./results/tables/nlinFstage_two.tex}
      &&&&\\ \midrule
      \multicolumn{5}{l}{\textbf{Panel B: Three Plus Sample}} \\
      \input{./results/tables/nlinFstage_three.tex}
      &&&&\\ \midrule
      \multicolumn{5}{l}{\textbf{Panel C: Four Plus Sample}} \\
      \input{./results/tables/nlinFstage_four.tex}
      \midrule
      \multicolumn{5}{p{12.2cm}}{{\footnotesize Notes: Each column reports the first stage estimate of fertility at each parity on twin births from the IV regressions displayed in Table \ref{TWINtab:nonlinearIV}. In each case we report the first stages for the baseline specification of the Non-Linear IV, although results are quantitatively similar in the case of the +S\&H specification. Standard errors are clustered by family (three plus and four plus samples), or robust to heteroscedasticity when only one child from each family is included in the regressions (two plus sample).}}
    \end{tabular}
  \end{center}
\end{table}

\begin{table}[htpb!]
  \caption{Assessing Bias with Covariate Adjustment -- Splitting Sample by Maternal Health}
  \label{TWINtab:MhealthQQ}
  \begin{center}
    \begin{tabular}{lcccccc}
      \toprule
      &\multicolumn{3}{c}{OLS} &\multicolumn{3}{c}{IV} \\ \cmidrule(r){2-4}\cmidrule(r){5-7}
      &Base&+H&+S\&H&Base&+H&+S\&H \\ \midrule
      \multicolumn{7}{l}{\textbf{Panel A: Developing Country Results}}\\
      \input{./results/tables/DHSpooled_health1.tex}
      \\
      \input{./results/tables/DHSpooled_health2.tex} \midrule
      \multicolumn{7}{l}{\textbf{Panel B: US Results}}\\
      \multicolumn{7}{l}{Dependent Variable = School Z-Score}\\
      \input{./results/tables/NHISpooled_EducationZscore_health1.tex}
      \\
      \input{./results/tables/NHISpooled_EducationZscore_health2.tex}
      \\
      \multicolumn{7}{l}{Dependent Variable = Excellent Health}\\
      \input{./results/tables/NHISpooled_excellentHealth_health1.tex}
      \\
      \input{./results/tables/NHISpooled_excellentHealth_health2.tex}
      \midrule
      \multicolumn{7}{p{15.4cm}}{{\footnotesize Notes: OLS and IV results are shown for the
          pooled 2+, 3+ and 4+ samples, splitting samples by the health status of each mother.
          In the case of IV estimates, fertility is instrumented using the twin instruments
          with pooling procedure described in \citet{Angristetal2010} and refinement discussed
          in \citet{MogstadWiswall2012}.
          In the developing country sample, less and more healthy refers to mothers whose height
          is respectively below and above the country-level mean (calculated in each survey) given
          heterogeneity in educational attainment by countries.  In the case of the US, more
          health refers to mothers who report being in excellent health, while less healthy
          refers to mothers who report any other health status. All other details follow OLS
          and IV estimates in Tables \ref{TWINtab:OLS}-\ref{TWINtab:NHISAll}.
          $^{*}$p$<$0.1; $^{**}$p$<$0.05; $^{***}$p$<$0.01.}}\\ \bottomrule
    \end{tabular}
  \end{center}
\end{table}

\begin{table}[htpb!]
  \caption{Bounds Estimates of the Quantity--Quality Trade-off}
  \label{TWINtab:boundsall}
  \begin{center}
    \begin{tabular}{lccccccc}
      \toprule
      &&\multicolumn{2}{c}{\citet{NevoRosen2012}} & \multicolumn{4}{c}{\citet{Conleyetal2012}} \\
      &IV&\multicolumn{2}{c}{Imperfect IV Bounds}&\multicolumn{2}{c}{UCI: $\gamma\in [0,2\hat\gamma]$}&\multicolumn{2}{c}{LTZ: $\mathcal{N}(\mu_\gamma,\sigma_\gamma^2)$}\\
      \cmidrule(r){3-4} \cmidrule(r){5-6} \cmidrule(r){7-8}
      &with Controls&Lower&Upper&Lower&Upper&Lower&Upper\\
      \midrule
      \multicolumn{8}{l}{\textbf{Panel A: DHS (Education Z-Score)}}\\
      \input{./results/tables/BoundsEstimates_DHS.tex}
      &&&&& \\ \midrule \multicolumn{8}{l}{\textbf{Panel B: USA (Education Z-Score)}}\\
      \input{./results/tables/BoundsEstimates_NHISEducationZscore.tex}
      &&&&& \\ \multicolumn{8}{l}{\textbf{USA (Excellent Health)}}\\
      \input{./results/tables/BoundsEstimates_NHISexcellentHealth.tex}
      \midrule\multicolumn{8}{p{16.4cm}}{\begin{footnotesize} Notes: This table presents upper and lower bounds of a 95\% confidence interval for the effects of family size on (standardised) children's educational attainment and health (health in USA only). \citet{NevoRosen2012} bounds are presented in columns 2 and 3, and variants of \citet{Conleyetal2012} bounds are presented in columns 4-7. the IV point estimate with full controls is displayed for comparison in column 1. \citet{NevoRosen2012} bounds are based on the assumption that selection into twinning and into fertility are oppositely signed (eg positive and negative), and twins are ``less endogenous'' than fertility.  \citet{Conleyetal2012} bounds are estimated as described in section \ref{TWINscn:gamma} under various priors about the direct effect that being from a twin family has on educational outcomes ($\gamma$). In the UCI (union of confidence interval) approach, it is assumed the true $\gamma\in[0,2\hat\gamma]$, while in the LTZ (local to zero) approach it is assumed that $\gamma$ follows the empirical distribution estimated in each case.  The preferred prior for $\gamma$ ($\hat\gamma$) and its distribution is discussed in \citet{BhalotraClarke2016}. Comparisons under a range of priors are presented in Figures \ref{TWINfig:PEx-DHS}-\ref{TWINfig:PEx-USA}.  Each estimate is based on the specifications with full controls from Tables \ref{TWINtab:DHSall} and \ref{TWINtab:NHISAll}.  \end{footnotesize}} \\ \bottomrule
    \end{tabular}
  \end{center}
\end{table}

\input{./results/added/Kitagawa.tex} 

\begin{landscape}\begin{table}[htpb!]
    \caption{Developing Country IV Estimates Using Same Sex Twins Only}\label{TWINtab:DHSsamesex}
    \begin{center}\begin{tabular}{lccccccccc}
        \toprule
        &\multicolumn{3}{c}{2+}&\multicolumn{3}{c}{3+}&\multicolumn{3}{c}{4+}\\ \cmidrule(r){2-4}\cmidrule(r){5-7} \cmidrule(r){8-10}
        &Base&+H&+S\&H&Base&+H&+S\&H&Base&+H&+S\&H\\ \midrule
        \multicolumn{10}{l}{\textbf{Panel A: First Stage}}\\
        \multicolumn{10}{l}{Dependent Variable = Fertility}\\
        \input{./results/tables/DHSsamesexIV_first.tex}
        \midrule
        \multicolumn{10}{l}{\textbf{Panel B: IV Results}}\\
        \multicolumn{10}{l}{Dependent Variable = School Z-Score}\\
        \input{./results/tables/DHSsamesexIV.tex} \midrule
        \multicolumn{10}{p{21.2cm}}{{\footnotesize Notes: Refer to notes to Table \ref{TWINtab:DHSall}.  This table follows identical specifications, however now only same sex twins are used as an instrument instead of all twins.  In the DHS, 64.1\% of twin pairs are of the same gender.  Standard errors are clustered by mother. $^{*}$p$<$0.1; $^{**}$p$<$0.05; $^{***}$p$<$0.01.}} \\
        \bottomrule \end{tabular} \end{center}
\end{table} \end{landscape}

\begin{landscape}\begin{table}[htpb!]
  \caption{US IV Estimates Using Same Sex Twins Only}\label{TWINtab:NHISsamesex}
  \begin{center}\begin{tabular}{lccccccccc}
      \toprule
      &\multicolumn{3}{c}{2+}&\multicolumn{3}{c}{3+}&\multicolumn{3}{c}{4+}\\ \cmidrule(r){2-4}\cmidrule(r){5-7} \cmidrule(r){8-10}
      &Base&+H&+S\&H&Base&+H&+S\&H&Base&+H&+S\&H\\ \midrule
      \multicolumn{10}{l}{\textbf{Panel A: First Stage}}\\
      \multicolumn{10}{l}{Dependent Variable = Fertility (School Z-Score Second Stage)}\\
      \input{./results/tables/NHISIVEducationZscore_samesex_first.tex}
      \\
      \multicolumn{10}{l}{Dependent Variable = Fertility (Excellent Health Second Stage)}\\
      \input{./results/tables/NHISIVexcellentHealth_samesex_first.tex}
      \midrule
      \multicolumn{10}{l}{\textbf{Panel B: IV Results}}\\
      \multicolumn{10}{l}{Dependent Variable = School Z-Score}\\
      \input{./results/tables/NHISIVEducationZscore_samesex.tex}
      \\
      \multicolumn{10}{l}{Dependent Variable = Excellent Health}\\
      \input{./results/tables/NHISIVexcellentHealth_samesex.tex}
      \midrule\multicolumn{10}{p{21.2cm}}{\begin{footnotesize} Notes: Refer to notes in Table \ref{TWINtab:NHISAll}. This table follows identical specifications, however now only same sex twins are used as an instrument instead of all twins.  In the NHIS, 66.0\% of twin pairs are of the same gender. Standard errors are clustered by mother. $^{*}$p$<$0.1; $^{**}$p$<$0.05; $^{***}$p$<$0.01.\end{footnotesize}} \\ \bottomrule
  \end{tabular}\end{center}\end{table}\end{landscape}

\begin{table}[htpb]
  \caption{Variable Definitions}
  \scalebox{0.97}{
  \begin{tabular}{lp{13cm}} \toprule
    Variable & Definition \\ \midrule
    \multicolumn{2}{l}{\textbf{Panel A: DHS Data}} \\
    School Z-score & Z-score of years of schooling, standardised relative to country and year of birth cohort. \\
    Male Child & Binary measure, one for boy, zero for girls \\
    Country & Fixed effect for country of survey  \\
    Year of Birth & Fixed effect for year of birth \\
    Child's Age& Fixed effect for child's age \\
    Contraceptive Intent & Fixed effect for mother's use of contraceptive methods  \\
    Mother's Age & Fixed effect for mother's age at child birth \\
    Mother's Age at First Birth & Inferred from age at survey time and age of child \\
    Mother's Education & Fixed effect for total years of education achieved \\
    Family Wealth & Fixed effect for DHS-assigned wealth quintile.  Where not recorded a separate fixed effect for ``no wealth quintile'' is included \\
    Mother's Height & Measured in centimetres \\
    Mother's BMI & Measured in units (weight in kilograms divided by height in metres squared) \\
    Prenatal Doctor Availability & Proportion of births in the same DHS cluster which received a prenatal check-up from a doctor \\
    Prenatal Nurse Availability & Proportion of births in the same DHS cluster which received a prenatal check-up from a nurse \\
    No Prenatal Care & Proportion of births in the same DHS cluster which received no prenatal check-ups from health professionals \\
    \multicolumn{2}{l}{\textbf{Panel B: NHIS Data}} \\
    Education Z-Score & Z-score of grade progression, standardised relative to month and year of birth cohort \\
    Excellent Health & Indicator of whether a child is classified by the family as being in ``excellent health'' (chosen from a categorical list) \\
    Male Child & Binary measure, one for boy, zero for girls \\
    Survey Year & Fixed effect for year NHIS wave was run \\
    Child Age & Fixed effect for age at interview in months and years \\
    Region & Fixed effect for census bureau region of residence \\
    Mother's Race & Fixed effect for mother's race \\
    Mother's Age & Fixed effect for mother's age in years \\
    Mother's Age at First Birth & Inferred from age at survey time and age of child \\
    Mother's Education & Fixed effects for mother's highest completed year of education \\
    Mother's Health Status & Self-reported based on categorical list \\
    Mother's Height & Mother's Height in Inches \\
    Smoking Status & Binary variable indicating whether the mother smoked prior to pregnancy \\
    Smoking Status Missing & Binary variable indicating no response to the mother's smoking status \\
    \bottomrule 
  \end{tabular}}
\end{table}
\clearpage

\begin{table}[htpb!]
  \begin{center}
    \caption{Manski and Pepper Monotone IV Bounds on Average Treatment Effect, DHS Data}
    \label{MIVDHS}
    \begin{tabular}{cccccccc} \toprule
      & &\multicolumn{3}{c}{Lower Bound on $\Delta(s,t)$} &\multicolumn{3}{c}{Upper Bound on $\Delta(s,t)$} \\ \cmidrule(r){3-5}\cmidrule(r){6-8} 
          &     & 0.025 Bootstrap & Bound    & 0.975 Bootstrap & 0.025 Bootstrap &  Bound   & 0.975 Bootstrap \\ 
      $s$ & $t$ & Quantile        & Estimate & Quantile        & Quantile        & Estimate & Quantile        \\ \midrule 
      \multicolumn{8}{c}{\textbf{Two-Plus Sample, Montone IV: Twin at Birth 2}} \\
      \input{./results/tables/ManskiPepperBounds.tex} \bottomrule
      \multicolumn{8}{p{17.2cm}}{{\footnotesize Notes: ATE bounds are presented following \citet{ManskiPepper2000},
          under \emph{only} a monotone IV assumption.  In each sample, the twin birth instrument is indicated, and
          our Monotone IV assumption is that investments in children are weakly higher among women
          with twin births than those with singleton births, given positive selection of women into twin
          births.  Here the outcome is a school z-score, and we assume $K_0=-3$ and $K_1=3$, each of
          which are extreme values in the outcome distribution.  Upper and lower bounds estimates are
          provided, along with 95\% confidence intervals on these bounds.  These are calculated with
          percentile bootstrap, with 500 bootstrap replications.
      }}
    \end{tabular}
  \end{center}
\end{table}

\begin{table}[htpb!]
  \begin{center}
    \caption{Manski and Pepper Monotone IV Bounds on Average Treatment Effect, USA Data}
    \label{MIVNHIS}
    \begin{tabular}{cccccccc} \toprule
      & &\multicolumn{3}{c}{Lower Bound on $\Delta(s,t)$} &\multicolumn{3}{c}{Upper Bound on $\Delta(s,t)$} \\ \cmidrule(r){3-5}\cmidrule(r){6-8} 
          &     & 0.025 Bootstrap & Bound    & 0.975 Bootstrap & 0.025 Bootstrap &  Bound   & 0.975 Bootstrap \\ 
      $s$ & $t$ & Quantile        & Estimate & Quantile        & Quantile        & Estimate & Quantile        \\ \midrule 
      \multicolumn{8}{l}{\textsc{PANEL A: Dependent Variable = School Z-Score}} \\
      \multicolumn{8}{c}{\textbf{Two-Plus Sample, Montone IV: Twin at Birth 2}} \\
      \input{./results/tables/ManskiPepperBounds_USeduc.tex}   \midrule 
      \multicolumn{8}{l}{\textsc{PANEL B: Dependent Variable = Excellent Health}} \\
      \multicolumn{8}{c}{\textbf{Two-Plus Sample, Montone IV: Twin at Birth 2}} \\
      \input{./results/tables/ManskiPepperBounds_UShealth.tex} \bottomrule
      \multicolumn{8}{p{17.2cm}}{{\footnotesize Notes: ATE bounds are presented following \citet{ManskiPepper2000},
          under \emph{only} a monotone IV assumption.  In each sample, the twin birth instrument is indicated, and
          our Monotone IV assumption is that investments in children are weakly higher among women
          with twin births than those with singleton births, given positive selection of women into twin
          births.  Here the outcome in panel A is a school z-score, and we assume $K_0=-3$ and $K_1=3$, each of
          which are extreme values in the outcome distribution. In panel B, the outcome is a binary
          variable for ``excellent health'', and so we assume $K_0=0$ and $K_1=1$. Upper and lower bounds
          estimates are
          provided, along with 95\% confidence intervals on these bounds.  These are calculated with
          percentile bootstrap, with 500 bootstrap replications.
      }}
    \end{tabular}
  \end{center}
\end{table}

\begin{table}[htpb!]
  \begin{center}
    \caption{Manski and Pepper MTS-MTR Lower Bounds on Average Treatment Effect, DHS Data}
    \label{MTS-MTRDHS}
    \begin{tabular}{cccc} \toprule
      & &\multicolumn{2}{c}{Lower Bound on $\Delta(s,t)$}  \\ \cmidrule(r){3-4}
          &     & 0.025 Bootstrap & Bound    \\
      $s$ & $t$ & Quantile        & Estimate \\ \midrule
      \multicolumn{4}{l}{\textbf{Two-Plus Sample, MTS--MTR Bounds}} \\
      \input{./results/tables/ManskiPepperMTSMTRBounds.tex} \bottomrule
      \multicolumn{4}{p{10.2cm}}{{\footnotesize Notes: ATE bounds are presented following \citet{ManskiPepper2000},
          under the MTS--MTR assumption.  These bounds conjecture that a fertility--human capital trade-off
          does exist, and as such, the upper bound is no larger than 0.  We present bounds for each of the
          parity-specific samples, providing the MTS--MTR lower bound, along with the confidence interval on the lower
          bound.   These are calculated with a
          percentile bootstrap, with 500 bootstrap replications.
      }}
    \end{tabular}
  \end{center}
\end{table}

\begin{table}[htpb!]
  \begin{center}
    \caption{Manski and Pepper MTS-MTR Lower Bounds on Average Treatment Effect, USA Data}
    \label{MTS-MTRNHIS}
    \begin{tabular}{cccc} \toprule
      & &\multicolumn{2}{c}{Lower Bound on $\Delta(s,t)$} \\ \cmidrule(r){3-4}
          &     & 0.025 Bootstrap & Bound    \\
      $s$ & $t$ & Quantile        & Estimate \\ \midrule
      \multicolumn{4}{l}{\textsc{PANEL A: Dependent Variable = School Z-Score}} \\
      \multicolumn{4}{l}{\textbf{Two-Plus Sample, MTS--MTR Bounds}} \\
      \input{./results/tables/ManskiPepperMTSMTRBounds_USeduc.tex}   \midrule 
      \multicolumn{4}{l}{\textsc{PANEL B: Dependent Variable = Excellent Health}} \\
      \multicolumn{4}{l}{\textbf{Two-Plus Sample, MTS--MTR Bounds}} \\
      \input{./results/tables/ManskiPepperMTSMTRBounds_UShealth.tex} \bottomrule
      \multicolumn{4}{p{10.8cm}}{{\footnotesize Notes: Notes: ATE bounds are presented following \citet{ManskiPepper2000},
          under the MTS--MTR assumption.  These bounds conjecture that a fertility--human capital trade-off
          does exist, and as such, the upper bound is no larger than 0.  We present bounds for each of the
          parity-specific samples and for each outcome variable of interest in US data (a school z-score and
          an excellent health indicator), providing the MTS--MTR lower bound, along with the confidence interval
          on the lower bound.   These are calculated with a percentile bootstrap, with 500 bootstrap replications.
      }}
    \end{tabular}
  \end{center}
\end{table}


\newpage
\bibliography{./BiBBase1}
\end{document}
